U.S. Pat. No. 6,745,129 discloses a wavelet-based method for analysis of singularities, wherein a wavelet transform is applied to seismic trace data. A so-called Hölder exponent, sometimes also known as Lipshitz exponent, is calculated for every time point of the wavelet transform for each seismic trace. Calculated Hölder exponents are then plotted against time.
Said US Pat. '129 calculates the Hölder exponent as the slope of a line found by linear least squares regression analysis, on a log-log plot, of a set of data points that represent wavelet coefficient versus scale for each localized time point. However, the data points do in tact show non-linear structure. Thus, the Hölder exponent as calculated is influenced by contributions arising from non-linearly scaling aspects embedded in the data.
In order to reduce the standard deviation of a liner regression line, US Pat. '129 proposes to eliminate from the data the large and small scale and select a mid-range of scales to subject to linear regression analysis. However, even in the selected mid-range of scales the wavelet coefficients do not appear to follow a linear relationship against scale.